Process transmitter with orthogonal-polynomial fitting

Abstract

A transmitter for measuring a process variable includes a sensor configured to couple to a process and having a sensor output related to the process variable. A microprocessor coupled to the sensor output provides a process variable output which is a function of an orthogonal-polynomial of the sensor output. A transmitter output is configured to provide an output related to the process variable.

What is claimed is:  
     
       1. A transmitter for measuring a process variable, comprising: 
       a sensor configured to couple to a process and having a sensor output related to the process variable;  
       a polynomial interpolator coupled to the sensor output having an interpolated process variable output which is a function of an orthogonal-polynomial used to interpolate the sensor output, wherein the orthogonal polynomial reduces power consumption by the polynomial interpolator;  
       a transmitter output configured to provide an output on a two-wire process control loop related to the interpolated process variable; and  
       a power module configured to couple to the two-wire process control loop and completely power the transmitter with power received from the two-wire process control loop.  
     
     
       2. The transmitter of  claim 1  wherein the orthogonal-polynomial comprises a Chebychev polynomial. 
     
     
       3. The transmitter of  claim 2  wherein terms T n (x) of the Chebychev polynomial obey a recursive formula and wherein T n (x) is n th  order Chebychev polynomial where n is the order of the Chebychev polynomial and x is related to the sensor output. 
     
     
       4. The transmitter of  claim 3  wherein the recursive formula is:              T   n                     (   x   )       =           (       2                   (     n   -   1     )       +   1     )     n                     T   1                     (   x   )                     T     n   -   1                       (   x   )       -         (     n   -   1     )     n                     (       N   2     -       (     n   -   1     )     2       )                     T     n   -   2                       (   x   )           ,     0   ≤   x   ≤     N   -   1                       
       where T is the Chebychev polynomial, x is related to the sensor output, n is representative of an order of the Chebychev polynomial and N is representative of a number of independent readings of the sensor output. 
     
     
       5. The transmitter of  claim 2  wherein the interpolated process variable is a function of at least two readings of the sensor output. 
     
     
       6. The transmitter of  claim 1  wherein the two-wire process control loop comprises a 4-20 mA two-wire process control loop. 
     
     
       7. The transmitter of  claim 1  wherein the polynomial interpolator comprises a microprocessor. 
     
     
       8. The transmitter of  claim 1  wherein the polynomial interpolator represents numbers using 32 data bits. 
     
     
       9. The transmitter of  claim 8  wherein the polynomial interpolator represents numbers using a 24 data bit mantissa. 
     
     
       10. The transmitter of  claim 1  wherein the polynomial interpolator uses floating point numbers. 
     
     
       11. The transmitter of  claim 1  wherein the polynomial interpolator uses integer numbers. 
     
     
       12. The transmitter of  claim 1  wherein the interpolated process variable output is an orthogonal-polynomial function of two sensor outputs. 
     
     
       13. The transmitter of  claim 12  wherein the two sensor outputs represent pressure and temperature. 
     
     
       14. The transmitter of  claim 12  wherein the interpolated process variable output comprises pressure. 
     
     
       15. The transmitter of  claim 1  wherein the interpolated process variable output is an orthogonal-polynomial function of three sensor outputs. 
     
     
       16. The transmitter of  claim 15  wherein the three sensor outputs represent differential pressure, absolute pressure and temperature. 
     
     
       17. The transmitter of  claim 16  wherein the interpolated process variable output comprises flow. 
     
     
       18. The transmitter of  claim 16  wherein the interpolated process variable output comprises density. 
     
     
       19. The transmitter of  claim 16  wherein the interpolated process variable output comprises a gas expansion coefficient. 
     
     
       20. The transmitter of  claim 1  wherein the orthogonal polynomial is normalized. 
     
     
       21. The transmitter of  claim 1  wherein the polynomial interpolator performs computation on integers to reduce power consumption. 
     
     
       22. A transmitter for measuring a process variable, comprising: 
       a sensor configured to couple to a process and having a sensor output related to the process variable;  
       a polynomial interpolator coupled to the sensor output having an interpolated process variable output which is a polynomial function of the sensor output, wherein terms of the polynomial function are functions of more than one exponential power of the sensor output, wherein the polynomial function reduces power consumption by the polynomial interpolator;  
       a transmitter output configured to provide an output on a two-wire process control loop related to the interpolated process variable; and  
       a power module configured to couple to the two-wire process control loop and completely power the transmitter with power received from the two-wire process control loop.  
     
     
       23. The transmitter of  claim 22  wherein the polynomial function comprises a Chebychev polynomial. 
     
     
       24. The transmitter of  claim 22  wherein the polynomial function comprises an orthogonal-polynomial. 
     
     
       25. The transmitter of  claim 22  wherein the two-wire process control loop comprises a 4-20 mA two-wire process control loop. 
     
     
       26. The transmitter of  claim 22  wherein the polynomial interpolator comprises a microprocessor. 
     
     
       27. The transmitter of  claim 22  wherein the polynomial function is normalized. 
     
     
       28. The transmitter of  claim 22  wherein the polynomial interpolator performs computation on integers to reduce power consumption. 
     
     
       29. A method performed by a process transmitter for measuring a process variable of a process, the method comprising: 
       sensing a parameter of the process related to the process variable and providing a sensor output related to the process variable;  
       approximating the process variable by interpolation using an orthogonal-polynomial applied to the sensor output to obtain an approximated process variable wherein the orthogonal polynomial reduces power consumption required by the approximating step;  
       outputting the approximated process variable on a two-wire process control loop; and  
       completely powering the transmitter with power received from the two-wire process control loop.  
     
     
       30. The method of  claim 29  wherein the orthogonal-polynomial comprises a Chebychev polynomial. 
     
     
       31. The method of  claim 30  wherein terms T n (x) of the Chebychev polynomial obey a recursive formula and wherein T n (x) is an n th  order Chebychev polynomial where n is the order of the Chebychev polynomial and wherein x is related to the sensor output. 
     
     
       32. The method of  claim 29  wherein approximating the process variable is a function of at least two sensor outputs from two different sensors. 
     
     
       33. The method of  claim 29  wherein approximating the process variable includes representing numbers using 32 data bits. 
     
     
       34. The method of  claim 29  wherein the approximated process variable is indicative of flow of process fluid. 
     
     
       35. The method of  claim 29  wherein the orthogonal polynomial is normalized. 
     
     
       36. The method of  claim 29  wherein the orthogonal polynomial allows integer computation to reduce power consumption required by the process transmitter. 
     
     
       37. A method for measuring a process variable in a process transmitter, comprising: 
       sensing a parameter of the process related to the process variable and providing a sensor output related to the process variable;  
       approximating the process variable using a polynomial function applied to the sensor output to obtain an approximated process variable, wherein terms of the polynomial function are functions of more than one exponential power of the sensor output wherein the polynomial function reduces power required by the approximating step;  
       outputting the approximated process variable on a two-wire wire process control loop; and  
       completely powering the process transmitter with power received from the two-wire process control loop.  
     
     
       38. The method of  claim 37  wherein the polynomial function comprises an orthogonal-polynomial. 
     
     
       39. The method of  claim 37  wherein the terms of the polynomial function obey a recursive formula. 
     
     
       40. The method of  claim 39  wherein the recursive formula is:              T   n                     (   x   )       =           (       2                   (     n   -   1     )       +   1     )     n                     T   1                     (   x   )                     T     n   -   1                       (   x   )       -         (     n   -   1     )     n                     (       N   2     -       (     n   -   1     )     2       )                     T     n   -   2                       (   x   )           ,     0   ≤   x   ≤     N   -   1                       
       where T is the Chebychev polynomial, x is related to the sensor output, n is representative of an order of the polynomial and N is representative of a number of independent readings of the sensor output. 
     
     
       41. The method of  claim 37  wherein approximating the process variable includes applying the polynomial function to more than one sensor output for more than one sensor. 
     
     
       42. The method of  claim 37  wherein the polynomial function allows integer computation to reduce power consumption required by the process transmitter. 
     
     
       43. A transmitter for measuring a process variable, comprising: 
       sensor means for providing a sensor output related to the process variable;  
       a polynomial interpolator means for determining an interpolated process variable as a function of an orthogonal-polynomial used to interpolate data from the sensor output, wherein the orthogonal polynomial reduces power consumption by the polynomial interpolator means;  
       an output means for communicating an output related to the interpolated process variable on a two-wire process control loop; and  
       a power module means for completely powering the transmitter with power from the two-wire process control loop.  
     
     
       44. A device for monitoring a process, the device measuring a process variable, comprising: 
       a sensor configured to couple to a process and having a sensor output related to the process variable;  
       a polynomial interpolator coupled to the sensor output having an interpolated process variable output which is a function of an orthogonal-polynomial used to interpolate the sensor output;  
       a device output configured to provide an output related to the interpolated process variable; and  
       wherein the polynomial interpolator performs computations using numerical integers with the orthogonal polynomial to reduce power consumption by the polynomial interpolator.  
     
     
       45. A device in a process control system for monitoring an industrial process, the device measuring a process variable, comprising: 
       a sensor configured to couple to a process and having a sensor output related to the process variable;  
       a polynomial interpolator coupled to the sensor output having an interpolated process variable output which is a polynomial function of the sensor output, wherein terms of the polynomial function are functions of more than one exponential power of the sensor output;  
       a device output configured to provide an output related to the interpolated process variable; and  
       wherein the polynomial interpolator performs computations using numerical integers with the polynomial function to reduce power consumption by the polynomial interpolator.